Questions and Answers
What means the same as $6 \times 5$?
What means the same as $6^5$?
What means the same as $3 + 3 + 3 + 3$?
What means the same as $2 + 2 + 2 + 2 + 2$?
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Identify the type of function graphed to the right.
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For an increase of 1 in the x-value, what is the increase in the y-value?
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Identify the type of function graphed to the right.
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As x increases by 1 unit, what is the exponential growth factor?
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What is the missing number in the table?
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Some of the graph is shown. The graph shows _______
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If the pattern continued, what value of y would be associated with x = 6?
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Which of the following situations represent linear growth? Check all that apply.
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Which of the following situations describe exponential growth? Check all that apply.
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Which growth pattern is represented in the table? (Link provided)
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Which growth pattern is represented in the table? (Link provided)
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Elisa puts $1,000 into each of 2 bank accounts. Account A: 3% interest rate, compounded annually, which is ___________ growth.
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Account B: $40 bonus added to the account each year, which is ___________ growth.
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How much money will be in Account A at the end of 3 years? $________
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How much money will be in Account B at the end of 3 years? $________
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If Elisa keeps the money in both accounts for 3 years, which account will yield more?
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If Elisa keeps the money in both accounts for 30 years, which account will yield more?
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Given a set of data, what steps would you take to identify whether the data showed linear or exponential growth?
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Study Notes
Linear Growth vs. Exponential Growth
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Equivalent Expressions:
- (6 \times 5) equates to 30.
- (6^5) equates to 7776.
- (3 + 3 + 3 + 3) simplifies to (4 \times 3) or 12.
- Repeated multiplication such as (2 \times 2 \times 2 \times 2 \times 2) leads to (2^5 = 32).
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Graphing Functions:
- Recognize the type of function in given graphs; distinctions between linear and exponential growth.
- An increase of 1 in the x-value may correspond to a specific increase in the y-value; for some functions, this could be constant (linear) or variable (exponential).
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Growth Factors:
- A specific exponential growth factor can apply when x increases by 1 unit, such as a value of 3.
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Missing Values and Patterns:
- Identifying missing numbers in sequences can determine patterns in growth; e.g., a missing number that fits a linear growth sequence might be 16, while projecting values for specific x-values aids in understanding growth trends.
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Identifying Growth Patterns:
- Linear growth scenarios include consistent additions, such as $40 yearly bonuses, while exponential growth involves increasing amounts, like compounding interest.
Financial Comparisons
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Account A vs. Account B:
- Account A earns interest at a 3% rate, representing exponential growth, while Account B demonstrates linear growth due to a fixed annual deposit.
- After 3 years, Account A's total is about $1092.73, while Account B totals $1120, making Account B the more lucrative choice in the short term.
- Over extended periods, such as 30 years, Account A will ultimately outperform Account B due to the nature of compound interest.
Data Analysis
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Identifying Growth Types:
- To determine if data reflects linear or exponential growth, begin by plotting the data points.
- Visual representation allows the observation of growth patterns: a straight trend indicates linear growth, while a steep rise suggests exponential growth.
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Description
Test your knowledge on the differences between linear and exponential growth. This quiz covers equivalent expressions, graphing functions, and identifying patterns in growth sequences. Sharpen your understanding of how these functions behave under various conditions.
